Solve for $x$ : $x^2 + 11x + 24 = 0$
The coefficient on the $x$ term is $11$ and the constant term is $24$ , so we need to find two numbers that add up to $11$ and multiply to $24$ The two numbers $8$ and $3$ satisfy both conditions: $ {8} + {3} = {11} $ $ {8} \times {3} = {24} $ $(x + {8}) (x + {3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 8) (x + 3) = 0$ $x + 8 = 0$ or $x + 3 = 0$ Thus, $x = -8$ and $x = -3$ are the solutions.